There's no magic antenna that can break the laws of physics and cover all bands with the same performance. Antennas are tuned to a specific frequency. However, the closest thing to an all band antenna is a discone. Though with a wideband antenna like a discone the gain is lower, and it is easier to overload the SDR with out of band strong signals.

In practice most omnidirectional antennas will receive something when used out of their design frequency.

NO! You can't beat physics since the receiver are much to wideband for a single passive antenna, if you want to receive also below 30 MHz than it's even more complicated.

Most antennas are very frequency selective (at best a few percent of the frequency)

Passive antennas are broader, but at best 1 to 2 octave (passive: Discone or directive log. periodic or similar designs)

Active antennas: are basically just short (to the wavelength) capacity connected to a preamp and can therefore cover a few decades.

Then there is antenna gain needed to receive the signal, which will depend on
- the polarization of the transmitted waves,
- the antenna pattern in azimuth and elevation to consider because
- frequencies below 30 MHz can be Radio Line of sight, ground or through ionospheric reflections,
- while >30 MHz it_s mainly Radio Line of sight
-propagation loss

Therefore no single antenna can fit all.

The broader an antenna is the more strong signal source will be fed to the receiver, resulting in degradation of receiver performance, unless you have filters/attenuaters to protect/relieve the receiver to allow it to function.